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In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split… (More)

A dominating set D in a graph is a subset of its vertex set such that each vertex is either in D or has a neighbour in D. In this paper, we are interested in an output-sensitive enumeration algorithm of (inclusionwise) minimal dominating sets in graphs, called Dom problem. It was known that this problem can be polynomially reduced to the well known… (More)

We reduce (in polynomial time) the enumeration of minimal dominating sets in interval and permutation graphs to the enumeration of paths in DAGs. As a consequence, we can enumerate in linear delay, after a polynomial time pre-processing, minimal dominating sets in interval and permutation graphs. We can also count them in polynomial time. This improves… (More)

It was proved independently and with different techniques in [Golovach et al.-ICALP 2013] and [Kanté et al.-ISAAC 2012] that there exists an incremental output polynomial algorithm for the enumeration of the minimal edge dominating sets in graphs, i.e., minimal dominating sets in line graphs. We provide the first polynomial delay and polynomial space… (More)

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal transversals in hypergraphs. We give a polynomial delay algorithm to list the set of minimal… (More)

- Alice Julien-Laferrière, Laurent Bulteau, Delphine Parrot, Alberto Marchetti-Spaccamela, Leen Stougie, Susana Vinga +2 others
- Scientific reports
- 2016

Synthetic biology has boomed since the early 2000s when it started being shown that it was possible to efficiently synthetize compounds of interest in a much more rapid and effective way by using other organisms than those naturally producing them. However, to thus engineer a single organism, often a microbe, to optimise one or a collection of metabolic… (More)

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of " set… (More)

The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded hypergraphs. Recent applications in computational biology however require to solve a generalization of this problem, that we… (More)